# A GTA Welding Cooling Rate Analysis on Stainless Steel and Aluminum Using Inverse Problems

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Thermal Model

_{m}:

_{∞}the room temperature.

_{xy}:

_{xy}. It has a Gaussian distribution and releases its energy continuously over the time as it moves with a constant positive velocity u in the x direction [2]:

#### 2.2. Aluminum 6065-T5

_{m}= 615 °C [13]. The thermal properties such as thermal conductivity, emissivity, thermal diffusivity, and specific heat were taken from fitting data points of Jensen et al. [14]. Further details on the experimental procedure, experimental data, and numerical code methodology can be seen in Magalhães et al. [9].

#### 2.3. Stainless Steel AISI 304L

_{m}= 1400 °C was obtained from International [16]. The thermal conductivity and thermal diffusivity curves were obtained from fitting data points in Touloukian et al. [17]. The AISI 304L emissivity curve was also obtained from fitting data points presented by Roger et al. [18].

#### 2.4. Numerical Analysis

## 3. Results and Discussion

#### 3.1. Aluminum 6065 T5

_{1}, T

_{2}, T

_{3}, and T

_{4}. The respective numerical temperature was calculated from the previously-developed C++ code [9] for the welding conditions t+ = 2 ms, t+ = 7 ms, t+ = 11 ms, and t+ = 13 ms. It must be pointed out that the highest temperatures are obtained by the thermocouples soon after the GTA arch is turned off at t = 24 s [9].

_{l}, local Nusselt number and h in any position on the plate.

_{l}on the surface of the plate. From the analysis of Figure 5, it may be noticed that Nu increases in the first seconds of the process and it stabilizes until the arch torch is turned off. After the process, the average Nu starts to increase again. This behavior is due to the non-linear characteristics of the thermal properties for air adopted in this study. It may also be noticed that Nu is not sensitive to the positive polarity. As the average temperature increases due to the positive polarity, the Nu number remains almost at the same value for all cases studied.

^{2}were used. Although the natural convection represents a large part of the overall cooling process, the heat loss by radiation significantly affects the cooling process while the GTA welding is performed. In Figure 7, for emissivity and heat transfer coefficient dependent on temperature, the heat rate loss by radiation reaches 311 W at t = 24 s while, at the same time, the heat rate loss by free convection is only 247 W. However, in this case, the heat rate loss by radiation decreases considerably when the TIG arch torch is turned off. For t = 140 s, the heat rate loss by radiation is only 13 W while by free convection is 53 W. For the case of ε = 0.2 and h = 20 W/m

^{2}, which are constant, the heat rate loss by radiation reaches 143 W at t = 24 s while, at the same time, by free convection it is 340 W. These values differ significantly from the values obtained for the temperature-dependent parameters. The heat loss by radiation for t = 24 s is underestimated in 168 W, while the free convection loss is overestimated in 93 W.

^{2}is adopted. The melting point is reached when t = 3.9 s. Before this point, the weld pool is not open. Thus, the heat lost by radiation and free convection in the weld pool is nearly zero. After this point, the analyzed parameter values start to increase. Due to the higher temperature of the weld pool, the heat loss, considering the transient emissivity, is more intense. However, those losses are not as expressive when compared to the heat losses of the plate. For instance, the higher radiation occurs at t = 24 s. At this point, the GTA torch is turned off. It may be seen that, at this instant, the heat loss by radiation in the FZ reaches only 1.3 W, while the losses by free convection in the FZ are even more negligible, at 0.3W. The calculated values for a constant emissivity and heat transfer coefficient differ from the non-linear parameters. The cooling rate by convection, in this case, is higher, 0.6 W. On the other hand, the cooling rate by convection is lower, 0.4 W. If the overall heat transfer losses are considered, the model with constant variables reaches the heat loss of 1.0 W at 24 s, while the non-linear model has a heat loss of l.6 W. In spite of the significant difference between both models, the calculated values for heat losses by convection and radiation do not have a large impact on the cooling process.

#### 3.2. Stainless Steel

^{2}K) after the arc torch is off, the stainless steel reaches only 9 (W/m

^{2}K). Figure 14 presents the evolution of the heat transfer coefficient for the stainless steel.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 10.**Evolution of the heat transfer coefficient, h (W/m

^{2}K), at instants (

**a**) 7.8 s, (

**b**) 15.6 s, (

**c**) 23.4 s, and (

**d**) 39.0 s for t+ = 2.0 ms.

**Figure 11.**The numerical thermal fields for GTA welding in (

**a**) stainless steel AISI 304L and (

**b**) aluminum 6065 T5.

**Figure 12.**Numerical temperature (T

_{num}) and experimental temperature (T

_{exp}) for GTA welding in stainless steel AISI 304L.

**Figure 14.**Evolution of the heat transfer coefficient, h (W/m

^{2}K), at instants (

**a**) 9.5 s, (

**b**) 19 s, (

**c**) 28.5 s, and (

**d**) 38.0 s for the GTA stainless steel welding.

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**MDPI and ACS Style**

Magalhaes, E.D.S.; Lima e Silva, A.L.F.d.; Lima e Silva, S.M.M.
A GTA Welding Cooling Rate Analysis on Stainless Steel and Aluminum Using Inverse Problems. *Appl. Sci.* **2017**, *7*, 122.
https://doi.org/10.3390/app7020122

**AMA Style**

Magalhaes EDS, Lima e Silva ALFd, Lima e Silva SMM.
A GTA Welding Cooling Rate Analysis on Stainless Steel and Aluminum Using Inverse Problems. *Applied Sciences*. 2017; 7(2):122.
https://doi.org/10.3390/app7020122

**Chicago/Turabian Style**

Magalhaes, Elisan Dos Santos, Ana Lúcia Fernandes de Lima e Silva, and Sandro Metrevelle Marcondes Lima e Silva.
2017. "A GTA Welding Cooling Rate Analysis on Stainless Steel and Aluminum Using Inverse Problems" *Applied Sciences* 7, no. 2: 122.
https://doi.org/10.3390/app7020122